基于维纳滤波的图像复原

100024。、、。TN911．73A1673－4793201104－0019－05ImageRestorationBasedonWienerFilteringJINFeiZHANGBinSIXuanYUANCong-xinSchoolofScienceCommunicationUniversityofChinaBeijing100024ChinaAbstractTheimprovedalgorithmofimagerestorationisproposedwhichbasedontheimagerestorationbyWienerfiltering.FirsttheWienerfilteringmethodisusedtoobtaintheinitialestimateofthedegradedimagethenusingtheinitialvaluetoreconstructtheimprovedWienerfilter．Andfilterthedegradedimageagain．Theexperimentalresultsshowthatthemethodhaslesscalculationtheadvantagesofhighprecisionandstronganti－noisecapability．AndtheimagerestorationresultsareimprovedsignificantlycomparedwiththeresultsobtainedbyusingtraditionalWienerfilters．Keywordsimagerestorationwienerfilteringpointspreadfunctionpeaksignal－to－noiseratio1。。。。。。1fxygxy。fxyHnxyf^。[e-mail]181/gxy=Hfxy+nxy。22．1·。。。f^xyfxyEf^xy－fxy2=minE。。2．2。。gxyfxynxy。f、g、nfxy、gxy、nxyQf。‖Qf^‖2‖g－Hf^‖2=‖n‖2‖g－Hf^‖2=‖n‖2Qf^f。。minJf^=‖Qf^‖2+λ‖g－Hf^‖2－‖n‖2λ。。f^Jf^f^=2QTQf^－2λHTg－Hf^=0f^QTQf^+λHTHf^g=01λQTQf^+HTHf^=HTgf^=HTH+sQTQ－1HTg1s=1λ。1。RfRnfnRf=EffTRn=EnnTRfijEfifjfij。fnRfRn20～30。RfRnRf=WAW－1Rn=WBW－1ABWABRfRn。。QTQR－1fRn1f^=HTH+sR－1fRn－1HTg2H=WDW－1HT=WD*W－1DHD*D。2f^=WD*DW－1+sWA－1BW－1－1WD*W－1gW－1W－1f^=DD*+sR－1fRn－1D*W－1gFuv=1Huv|Huv|2|Huv|2+s·PnuvPfuvGuv3024。GuvHuv|Huv|2=H*uv·HuvH*uvHuvPnuv=|Nuv|2Pfuv=|Fuv|2s=1λλ。2．3Hwuv=1Huv|Huv|2|Huv|2+s·PnuvPfuv。|Nuv|2Hwuv=1Huv|Huv|2|Huv|2+KK。K≈PnuvPfuvK≈=1MN∑u∑vPnuv1MN∑u∑vPfuv=∑u∑vPnuv∑u∑vPfuv。33．1。。2FMuv=H*uv|Huv|2+σ2n/P*fuvGuv4P*fσ2n。。n=Enxy=1MN∑Mx=1∑Ny=1nxyσ2n=Enxy－n21MN∑Mx=1∑Ny=1nxy－n2nxyσ2nf^xyσ2n=1MN∑xygxy－f^xy·hxy23．21。PSFPSF。2。nxy。2。33P*fuvσ2n。44。3。4PSFx0ty0txyTgxygxv=∫T0fx－x0ty－y0tdt1218Guv=∫∞－∞∫∞－∞gxyei2πux+vydxdy=∫∞－∞∫∞－∞∫∞－∞fx－x0ty－y0tdte－i2πux+vydxdyGuv=∫∞－∞∫∞－∞∫∞－∞fx－x0ty－y0te－i2πux0t+vy0tdtGuv=∫T0Fuve－i2πux0t+vy0tdt=Fuv∫T0e－i2πux0t+vy0tdtHuv=∫T0e－i2πux0t+vy0tdtGuv=HuvFuvx0ty0tHuv=∫T0e－i2πux0t+vy0tdt2045°。Lena0．0022。。RPSNRPSN=101g2552MN/∑Mx=1∑Ny=1fxy－f^xyfxyMNf^xy。σ2n=0.00249．604861．1735。。。5224。。。PSF。。。1.M．．2005．2．J．200408．3.M．2006．4．WienerJ．200703．5．J．200611．585MVuAPauraj．OptimalLinearPrecodersforMIMOWirelessCorrelatedChannelswithNon－zeroMeaninSpace－TimeCodedSystemsJ．IEEETransonSignalProcessing5462006．6MVuAPaulraj．OntheCapacityofMIMOWirelessChannelswithDynamicCSITJ．IEEEJournalonSelectedAreasinCommunications2572007．32